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Insights from a workshop on gamification of research in mathematics and computer science

Alexis Langlois-Rémillard, Élise Raphael, Erika Roldan

TL;DR

This work introduces the approach to the gamification of research in mathematics and computer science through three illustrative examples and provides insights into what makes the proposed gamification effective for three research topics in discrete and computational geometry and topology.

Abstract

Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations and provide insights into what makes our proposed gamification effective for three research topics in discrete and computational geometry and topology: (1) DominatriX, an art gallery problem involving polyominoes with rooks and queens; (2) Cubical Sliding Puzzles, an exploration of the discrete configuration spaces of sliding puzzles on the $d$-cube with topological obstructions; and (3) The Fence Challenge, a participatory isoperimetric problem based on polyforms. Additionally, we report on the collaborative development of the game Le Carré du Diable, inspired by The Fence Challenge and created during the workshop Let's talk about outreach!, held in October 2022 in Les Diablerets, Switzerland. All of our outreach encounters and creations are designed and curated with an inclusive culture and a strong commitment to welcoming the most diverse audience possible.

Insights from a workshop on gamification of research in mathematics and computer science

TL;DR

This work introduces the approach to the gamification of research in mathematics and computer science through three illustrative examples and provides insights into what makes the proposed gamification effective for three research topics in discrete and computational geometry and topology.

Abstract

Can outreach inspire and lead to research and vice versa? In this work, we introduce our approach to the gamification of research in mathematics and computer science through three illustrative examples. We discuss our primary motivations and provide insights into what makes our proposed gamification effective for three research topics in discrete and computational geometry and topology: (1) DominatriX, an art gallery problem involving polyominoes with rooks and queens; (2) Cubical Sliding Puzzles, an exploration of the discrete configuration spaces of sliding puzzles on the -cube with topological obstructions; and (3) The Fence Challenge, a participatory isoperimetric problem based on polyforms. Additionally, we report on the collaborative development of the game Le Carré du Diable, inspired by The Fence Challenge and created during the workshop Let's talk about outreach!, held in October 2022 in Les Diablerets, Switzerland. All of our outreach encounters and creations are designed and curated with an inclusive culture and a strong commitment to welcoming the most diverse audience possible.

Paper Structure

This paper contains 35 sections, 3 theorems, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Two examples of gamification
  3. DominatriX
  4. Setup
  5. Content
  6. Goals for advanced audiences
  7. Cubical Sliding Puzzles
  8. Setup
  9. Content
  10. Goals for advanced audiences
  11. Design choices
  12. The Fence Challenge and the game Le Carré du Diable
  13. Genesis of the problem: pentomino fence
  14. New results on extremal fence problems
  15. The game -- Le Carré du Diable
  16. ...and 20 more sections

Key Result

Lemma 3.2

If the pentomino fence is isotopic to the circle, then it can be placed on a $20\times 20$ board.

Figures (11)

  • Figure 1: Left, a corner-connection, not closing the fence; right an edge-connection with the rook-movement
  • Figure 2: A tentative of tetromino fence (without the "o").
  • Figure 3: Screenshot from a level of the video game Queens and Rooks Domination accessible at https://www.erikaroldan.net/queensrooksdomination. (The solution is 7 queens.)
  • Figure 4: Screenshot of a cube-level from the video game Cubical Sliding Puzzle, available at https://www.erikaroldan.net/cubical-sliding-puzzles. The highlighted nodes represent the possible moves for the selected green rings.
  • Figure 5: All the twelve pentominoes.
  • ...and 6 more figures

Theorems & Definitions (5)

  • Definition 3.1
  • Lemma 3.2
  • Proposition 3.3
  • Proposition A.1
  • proof